In January 2015 I earned a Ph.D. degree at the Dept. of Statistics and Operations Research of the Polytechnic University of Catalonia (Barcelona, Spain) with a dissertation titled Mathematical programming based approaches for classes of complex network problems, where I proposed and developed an optimization based framework for the statistical inference and analysis of individual decisions under network constraints and effects.

Despite my affiliation to an operations research department of a polytechnic university, my passion for the mathematical beauty and for any form of intellectual recklessness drove my research orientation to underestimate the practical advantage of applied research, during my PhD period. Therefore, I would now regard my PhD thesis as a contribution to the mathematical sociology, more than a contribution to the operations research.

The Department of Statistics and Operations Research at the Polytechnic University of Catalonia is an "engineering oriented" department (with approx 40 permanent members, whose research works pivot mainly on the industrial engineering, the development of intelligent interfaces and automatic data processing, optimization and simulation of flows in networks). It was created in 1987 as a result of the University Reform Law, bringing together diverse groups of the university that until then had been working separately in the areas of the statistics and operations research.

My PhD thesis work has been framed within the research contribution of the Group of Numerical Optimization and Modeling (GNOM), under the supervision of Jordi Castro, one of the European top researchers in large-scale computational optimization.

In this section of my blog you will find a collection of documents that originate from the six chapters of my PhD thesis.

Thesis documents

Dissertation abstract

Full manuscript

Computer programs and data sets

Chapter I
  • No program used.

Chapter II
  • R codes (Sections 2.1, 2.2, 2.3, 2.4);
  • AMPL codes (Section 2.4);
  • Data (Section 2.3):
    • Berdnard and Killworth fraternity;
    • Berdnard and Killworth office;
    • Kapferer Tailor shop (first period);
    • Kapferer Tailor shop (second period);
    • Dolphins' social network;
    • Newman scientific collaboration;
    • Florentine Reminiscence families;
    • Kapferer's mine;

Chapter III
  • R codes;
  • Matlab codes;
  • BlockIP;

Chapter IV

  • Matlab codes;
  • BlockIP;

Chapter V

  • Matlab codes;
  • BlockIP;

Chapter VI
  • Java codes;
  • Data:
    • Endowments-preference simulated data (Subsection 6.3.1);

Peer-reviwed pubblications

  • Castro J., Nasini S., (2015), Mathematical programming approaches for classes of random network problems, European Journal of Operational Research (link).
  • Nasini S., Castro J., Fonseca P., (2015), A Mathematical programming approach for different scenarios of bilateral bartering, Statistics and Operation Research Transactions. (link).
  • Castro J., Nasini S., (2015), Preconditioning IPMs for classes of primal-blocks angular problems, under review in Mathematical Programming.
  • Nasini S., Castro J., Fonseca P., (2013), Novel representation of network structures by spectral theory consideration, under review in Social Networks.

Invited conferences


IFORS-2014 (Barcelona, Spain) 

Abstract. The application of Mathematical programming based approaches in the field of random graph represents a novel and generally unexplored research area. Random graphs is the general term to refer to probability distributions over families of networks. As closed-form probabilistic models of networks are often not available, the ability of randomly generating networks verifying specific constraints might be useful to reconstruct the empirical distribution of network features -- clustering coefficient, average path length, assortativity coefficient, etc. --. Based on the characterization of families of networks by means of systems of linear constraints -- which is done by proving the total unimodularity of the associated coefficient matrices--, we asses that linear-programming-based approaches might provide highly efficient ways to randomly generate networks with fixed structural features. This is particularly true when a specialized interior point algorithm for primal-block angular problems is used. By taking into account the matrix structure of the resulting LPs, the reduced computational complexity of the specialized interior point algorithm can be mathematically proved for this class of problems. In addition, a closed-form probability distribution associated to the LP based network generation process can be mathematically derived, by the KKT conditions of the LP associated to the aforementioned families of networks. 

Key words: Linear Programming, Interior Point Methods, Preconditioned Conjugate Gradient, Random Graphs, Complex networks.


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Preconditioning IPMs for block-angular problems with "almost linearly dependent" constraints

Abstract. One of the most efficient interior-point methods for some classes of primal-block angular problems solves the normal equations by a combination of Cholesky factorizations and preconditione d conjugate gradient for, respectively, the block and linking constraints. We show that the principal angles between the subspaces generated by the diagonal blocks and the linking constraints play an important role in the proper choice of the preconditioner. Under these considerations we propose an easily computable preconditioner which results to be particularly effective when the principal angles between the subspaces generated by the diagonal blocks and the linking constraints are small, that is to say, when the linking constraints are almost linearly dependent with the block constraints. This preconditioner resulted to be complementary to the currently available power series preconditioner for block angular problems: the smaller the principal angles are, the more the power series preconditioner is outperformed by the new preconditioner. Computational results will be presented.

Key words: Interior Point Methods, Linear Programming, Preconditioned Congiugate Gradient.


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Generating random networks by linear programming approaches

Abstract.Social networks is a recent area of research motivated by the empirical study of real-world networks, such as social relations, protein interaction, neuronal connections, etc. As closed-form probabilistic models of networks are often not available, the ability of randomly generating networks verifying specific constraints might be useful. The purpose is to develop optimization-based procedures to randomly generate networks with structural constraints, within the probabilistic framework of conditional uniform models. Based on the characterization of families of networks by means of systems of linear constraints, polynomial-time methods to generate networks with specified structural properties are constructed. The computational results suggest that the proposed methods can represent a general framework for the efficient simulation of random networks even beyond the models analyzed in this Master Thesis.

Key words: Random Graphs, Social networks, Linear Programming, KKT conditions, Central Path.


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Generating conditional uniform random networks by optimization procedures

Abstract.Complex networks is a recent area of research motivated by the empirical study of real-world networks, such as social relations, protein interaction, neuronal connections, etc. As closed-form probabilistic models of networks are often not available, the ability of randomly generating networks verifying specific constraints might be useful. The purpose of this work is to develop optimization-based procedures to randomly generate networks with structural constraints, within the probabilistic framework of conditional uniform models. Based on the characterization of families of networks by means of systems of linear constraints, polynomial-time methods to generate networks with specified structural properties are constructed.

Key words: Random Graphs, Social Networks, Linear Programming, Total Unimodularity.